Coordinate Planes and Graphing

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Questions and Answers

A vertical line passes through the point (3, 6). Select all points that lie on the vertical line.

  • (10, 6)
  • (3, 8) (correct)
  • (9, 6)
  • (3, 10) (correct)
  • (1, 6)
  • (3, 2) (correct)

Plot (4, 5) in this coordinate plane.

See the coordinate plane in the original document.

A vehicle can travel 20 miles on each gallon of gas. Complete the table. Gasoline (gallons) 1 2 3 4 5 Distance (miles) 20 _____ _____ _____ _____

40, 60, 80, 100

Make a line graph of the data.

<p>See line graph of the data in the original document.</p> Signup and view all the answers

The table shows the number of bagels sold by a street vendor each day for 7 days. Day 1 2 3 4 5 6 7 Number of Bagels Sold 7 10 10 7 5 8 9 On how many days were less than 8 bagels sold? _____ day(s)

<p>3</p> Signup and view all the answers

Which expression can you use to find the distance between points (6, 2) and (10, 2)?

<p>10 - 6 (C)</p> Signup and view all the answers

What is the distance between points (6, 2) and (10, 2)? _____ units

<p>4</p> Signup and view all the answers

Between which two years did the number of participants increase the most? between years _____ and _____

<p>1, 2</p> Signup and view all the answers

To make a cleaning solution, you mix 4 cups of vinegar and 2 cups of rubbing alcohol with each gallon of water. Complete the table. Water (gallons) 1 2 3 4 5 Vinegar (cups) 4 8 ____ ____ ____ Rubbing Alcohol (cups) 2 4 ____ ____ ____

<p>12, 16, 20, 6, 8, 10</p> Signup and view all the answers

Which statement describes the relationship between the number of cups of rubbing alcohol and the number of cups of vinegar?

<p>The number of cups of rubbing alcohol is $\frac{1}{2}$ the number of cups of vinegar. (C)</p> Signup and view all the answers

Use this graph to find the distance traveled in 5 hours. _____ miles

<p>300</p> Signup and view all the answers

Which statement correctly interprets a point in this coordinate plane?

<p>It costs $6 to park for 2 hours. (D)</p> Signup and view all the answers

Write the ordered pair that corresponds to each point in this coordinate plane. Point A: ( _____, _____ )

<p>5, 4</p> Signup and view all the answers

Flashcards

x-coordinate

A point's horizontal position on a coordinate plane.

y-coordinate

A point's vertical position on a coordinate plane.

Coordinate Plane

A grid formed by two perpendicular lines used to locate points, which are the x-axis and y-axis.

Ordered Pair

A pair of numbers (x, y) that specifies the location of a point in a coordinate plane.

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Line Graph

A graph that uses points connected by line segments to show changes in data over time.

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Vertical Line

A straight line where all points have the same x-coordinate.

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Study Notes

  • These notes cover coordinate planes, graphing data, and understanding relationships between points and data sets.

Vertical Lines and Points

  • A vertical line passing through the point (3, 6) includes all points with an x-coordinate of 3.
  • Points that lie on this vertical line have the form (3, y), where y can be any value.

Plotting Points on a Coordinate Plane

  • To plot a point (x, y) on a coordinate plane, find the x-coordinate on the horizontal axis and the y-coordinate on the vertical axis.
  • Mark the point where the two values intersect.

Completing a Table with Proportional Data

  • If a vehicle travels 20 miles on each gallon of gas, the distance traveled is proportional to the number of gallons used.
  • To find the distance for a given number of gallons, multiply the number of gallons by 20 as the rate is 20 miles per gallon.

Creating a Line Graph from a Table

  • To create a line graph, plot each data point from the table on the coordinate plane.
  • Connect the points with lines to show the relationship between the two variables.

Graphing Data in a Coordinate Plane

  • Each day's bagel sales can be represented as a point (day, number of bagels sold).
  • Plot these points on a coordinate plane with the day on the x-axis and the number of bagels sold on the y-axis.

Distance Between Two Points

  • To find the horizontal distance between two points (x1, y) and (x2, y) with the same y-coordinate, subtract the x-coordinates.
  • The distance between points (6, 2) and (10, 2) can be found using the expression 10 - 6.

Analyzing Data in a Table

  • The table shows the number of participants in a dance competition over several years.
  • To find the years with the largest increase, calculate the difference in the number of participants between consecutive years.
  • Identify the largest difference to determine the years with the most growth.

Understanding Relationships in Cleaning Solutions

  • The cleaning solution mixes 4 cups of vinegar and 2 cups of rubbing alcohol per gallon of water.
  • The amount of rubbing alcohol is half the amount of vinegar (2 is 1/2 of 4).
  • This proportional relationship remains constant regardless of the number of gallons.

Interpreting Graphs

  • The graph shows the distance traveled over time; to find the distance traveled in 5 hours, locate 5 hours on the x-axis and find the corresponding distance on the y-axis.
  • By interpreting a point, determine the cost for the amount of time parked.

Identifying Coordinates on a Coordinate Plane

  • Each point on a coordinate plane is represented by an ordered pair (x, y), where x is the horizontal position and y is the vertical position.
  • To find the coordinates of a point, locate its position on the x-axis and the y-axis.

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